Question: Simplify the following expression: $ y = \dfrac{-1}{7} - \dfrac{8}{a - 5} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{a - 5}{a - 5}$ $ \dfrac{-1}{7} \times \dfrac{a - 5}{a - 5} = \dfrac{-a + 5}{7a - 35} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{8}{a - 5} \times \dfrac{7}{7} = \dfrac{56}{7a - 35} $ Therefore $ y = \dfrac{-a + 5}{7a - 35} - \dfrac{56}{7a - 35} $ Now the expressions have the same denominator we can simply subtract the numerators: $y = \dfrac{-a + 5 - 56 }{7a - 35} $ Distribute the negative sign: $y = \dfrac{-a + 5 - 56}{7a - 35}$ $y = \dfrac{-a - 51}{7a - 35}$